The second essential ingredient for such calculations, besides the emissivity, is the description of the fireball evolution in the T– \(\mu _B\)  plane.
The reference calculations to describe the expansion of the collision zone in reactions at ultra-relativistic energies are solutions of relativistic hydro-dynamics with suited definitions of the initial thermalized state.
Such calculations are very involved and CPU-hungry and go well beyond simple descriptions to study thermal dilepton radiation (for details see e.g. [1]}, [2]}).
For systematic studies of thermal radiation, over a wide range in beam energy, a common (simplified) strategy is to define an initial volume of cylindrical shape (following the concept of boost invariance) with given initial energy density and chemical potentials.
The dynamics of the fireball is then obtained by implying isentropic expansion and using a partonic as well as a hadronic equation-of-state for the QGP and hadronic phase, respectively.
Details of such an expansion model can be found e.g. in [3]}).
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